Modelling Group Heterogeneity for Small Area Estimation Using <i>M</i>‐Quantiles

Dawber, James; Chambers, Ray

doi:10.1111/insr.12284

Cited by 5 publications

(6 citation statements)

References 19 publications

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“…This is an attractive non-parametric procedure for small area estimation because there are no random effects to model, but random effects come out as summaries of q-scores. A good review paper is given by Dawber and Chambers [15]. This is directly related to the procedure mentioned above.…”

Section: Iterative Re-weighted Least Squares Methodsmentioning

confidence: 99%

Section: Bayesian Projective Inferencementioning

confidence: 99%

“…For the non-sampled households in non-sampled wards (areas), we use the IRLS estimates at x ˜ ij β ˜.5 ; see Dawber and Chambers [15]. For non-sampled households in a sampled ward, we use an average of the quantiles corresponding to the sampled households; see Dawber and Chambers [15]. For the NER model, we would need to use x ˜ ij β ˜+ ν i for the non-sampled households within sampled wards via the posterior samples of the ν i (already drawn).…”

Section: Bayesian Projective Inferencementioning

confidence: 99%

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A Bayesian Approach to Linking a Survey and a Census via Small Areas

Nandram

2021

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We predict the finite population proportion of a small area when individual-level data are available from a survey and more extensive household-level (not individual-level) data (covariates but not responses) are available from a census. The census and the survey consist of the same strata and primary sampling units (PSU, or wards) that are matched, but the households are not matched. There are some common covariates at the household level in the survey and the census and these covariates are used to link the households within wards. There are also covariates at the ward level, and the wards are the same in the survey and the census. Using a two-stage procedure, we study the multinomial counts in the sampled households within the wards and a projection method to infer about the non-sampled wards. This is accommodated by a multinomial-Dirichlet–Dirichlet model, a three-stage hierarchical Bayesian model for multinomial counts, as it is necessary to account for heterogeneity among the households. The key theoretical contribution of this paper is to develop a computational algorithm to sample the joint posterior density of the multinomial-Dirichlet–Dirichlet model. Specifically, we obtain samples from the distributions of the proportions for each multinomial cell. The second key contribution is to use two projection procedures (parametric based on the nested error regression model and non-parametric based on iterative re-weighted least squares), on these proportions to link the survey to the census, thereby providing a copy of the census counts. We compare the multinomial-Dirichlet–Dirichlet (heterogeneous) model and the multinomial-Dirichlet (homogeneous) model without household effects via these two projection methods. An example of the second Nepal Living Standards Survey is presented.

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Section: Iterative Re-weighted Least Squares Methodsmentioning

confidence: 99%

Section: Bayesian Projective Inferencementioning

confidence: 99%

Section: Bayesian Projective Inferencementioning

confidence: 99%

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A Bayesian Approach to Linking a Survey and a Census via Small Areas

Nandram

2021

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“…regions or provinces), when sample sizes are too small for precise direct estimation (Rao & Molina, 2015). We broadly focus on two general approaches to SAE models, the mixed model approach and the

M

‐quantile approach, see Dawber and Chambers (2019) for a recent review and comparison of these two approaches. In this section we first present the mixed model approach to SAE for multi‐category data, before presenting the application of ME regression using the

M

‐quantile approach.…”

Section: Sae For Multi‐category Datamentioning

confidence: 99%

Expectile Regression for Multi-Category Outcomes with Application to Small Area Estimation of Labour Force Participation

Dawber

Salvati

Fabrizi

et al. 2022

Journal of the Royal Statistical Society Series A: Statistics in Society

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In many applications of small area estimation, dichotomous or categorical outcomes are the targets of statistical inference. For example, in the analysis of labour markets, proportions of working‐age people in the various labour market statuses are of interest. In this paper, in line with the recent literature, we consider a classification with more than three statuses and estimate related population parameters for 611 local labour market areas using data from the 2012 Italian Labour Force Survey, administrative registers and the 2011 Census. As for the methodology, we propose multinomial expectile regression models. These models provide a means to utilise M$$ M $$‐quantile type approaches, which have been shown to be a useful alternative to mixed model approaches when parametric assumptions on the distribution of random effects cannot be met. Via a large‐scale simulation study, we show how this novel approach is much faster and provides reliable results when compared to multinomial mixed model approaches, and works for any number of categories rather than just a small number of categories as is more commonly the case with existing methods. Furthermore, the proposed approach potentially provides a framework for developing other methods for prediction with multi‐category outcomes.

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“…The most prominent field of application for MQ regression is in small area estimation (SAE), see Dawber and Chambers (2019) for an overview of these methods. Chambers and Tzavidis (2006) showed that MQ regression models perform comparably to traditional SAE models using mixed models, and perform better when outliers are present in the data.…”

Section: Introductionmentioning

confidence: 99%

Scale estimation and data-driven tuning constant selection for M-quantile regression

Dawber,

Salvati,

Schmid

et al. 2020

Preprint

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M-quantile regression is a general form of quantile-like regression which usually utilises the Huber influence function and corresponding tuning constant. Estimation requires a nuisance scale parameter to ensure the M-quantile estimates are scale invariant, with several scale estimators having previously been proposed. In this paper we assess these scale estimators and evaluate their suitability, as well as proposing a new scale estimator based on the method of moments. Further, we present two approaches for estimating data-driven tuning constant selection for M-quantile regression. The tuning constants are obtained by i) minimising the estimated asymptotic variance of the regression parameters and ii) utilising an inverse M-quantile function to reduce the effect of outlying observations. We investigate whether data-driven tuning constants, as opposed to the usual fixed constant, for instance, at c=1.345, can improve the efficiency of the estimators of M-quantile regression parameters. The performance of the data-driven tuning constant is investigated in different scenarios using model-based simulations. Finally, we illustrate the proposed methods using a European Union Statistics on Income and Living Conditions data set.

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Modelling Group Heterogeneity for Small Area Estimation Using M‐Quantiles

Cited by 5 publications

References 19 publications

A Bayesian Approach to Linking a Survey and a Census via Small Areas

A Bayesian Approach to Linking a Survey and a Census via Small Areas

Expectile Regression for Multi-Category Outcomes with Application to Small Area Estimation of Labour Force Participation

Scale estimation and data-driven tuning constant selection for M-quantile regression

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